MinT - Best Known (14, 14+55, s)-Nets in Base 128

Best Known (14, 14+55, s)-Nets in Base 128

(14, 14+55, 288)-Net over F₁₂₈ — Constructive and digital

Digital (14, 69, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 69, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(14, 14+55, 353)-Net over F₁₂₈ — Digital

Digital (14, 69, 353)-net over F₁₂₈, using

net from sequence [i] based on digital (14, 352)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 14 and N(F) ≥ 353, using
  - a curve from the manYPoints database [i]

(14, 14+55, 17430)-Net in Base 128 — Upper bound on s

There is no (14, 69, 17431)-net in base 128, because

1 times m-reduction [i] would yield (14, 68, 17431)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 195120 730693 938209 563934 464921 450323 776728 771592 390652 756174 592057 672911 435222 083359 870727 787726 084509 061045 913177 627221 653074 844601 408471 162368 > 128⁶⁸ [i]